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The urgent task of modern energy is to ensure reliable and efficient power supply to consumers, even those located in remote, far end places. A hybrid energy system with renewable energy sources is a promising way to ensure such a process. A characteristic feature of the modes of such systems, especially with high penetration levels of renewable energy sources, is the presence of ripples in the charge–discharge currents of the batteries used as energy storage devices. Batteries operation with such current fluctuations leads to rapid degradation of its characteristics as well as a reduction in its lifetime. Furthermore, it leads to a decrease in the reliability of the power supply system and an increase in the cost of generated electricity. A significant drawback of hybrid systems built according to well-known standard schemes is the inefficient use of the primary renewable energy, which is especially critical for energy systems located geographically in areas with severe climatic conditions. This article proposes a new construction method and an algorithm for controlling the modes of hybrid energy systems based on a dual-circuit energy storage device, which increases their reliability and energy efficiency. The prominent outcomes of operating modes of a hybrid power plant with a high penetration of renewable sources are presented, which proves that the proposed method of construction and the proposed control algorithm provide reliable and efficient control of the power balance of the hybrid power system in all possible operating conditions. In addition, the overall efficiency of the proposed renewable energy system is increased from 28% to 60% compared to standard hybrid power plants.